There was no immediate word on the cause of Geldof's death at her home in Wrotham, Kent, southeast England, but police called it "unexplained and sudden."
In a family statement, Bob Geldof said: "Peaches has died. We are beyond pain."
Peaches Geldof had acknowledged using drugs in the past but said in a 2009 interview that she had quit.
The news of her death came as a shock to Britain's entertainment and fashion circles, where Geldof had been active as a model, television presenter and fashion writer. She was a frequent attendee at fashion shows in London and New York, and was photographed just last week at a London show for the Tesco brand F&F.
Geldof was only 11 when her mother, television presenter Paula Yates, died of a drug overdose in 2000, and those who knew her said it hit her extremely hard.
Her last message on Twitter came on Sunday, when she posted a photograph of herself as a toddler next to her mother along with the caption: "Me and my mum."
Her father issued an anguished statement Monday from the family about her death.
"She was the wildest, funniest, cleverest, wittiest and the most bonkers of all of us," he wrote. "Writing 'was' destroys me afresh. What a beautiful child. How is this possible that we will not see her again? How is that bearable? We loved her and will cherish her forever."
The statement was signed by Bob, Jeanne (his partner), Peaches' sisters Fifi and Pixie and her half-sister Tiger Geldof.
Kent police declined to name Geldof, but when asked about her death they said in a statement that officers were called to a house near Wrotham following a report of concern for a woman's welfare Monday afternoon. They said the 25-year-old woman was pronounced dead by emergency officers and that the death was being treated as "unexplained and sudden."
In an interview with the Guardian newspaper in 2009, Geldof acknowledged that she used drugs as a teenager but said she had stopped.
"'Yeah, I've taken drugs. Yes, I have had experiences, and a few of those experiences were unsavory, not ones I want to repeat, but I was growing up. I wanted the experience," she told the paper.
"I wasn't hugely into drugs and I'm sober now," she added. "I'm not Amy Winehouse. I never have been. I wasn't a crackhead."
Peaches Geldof was married twice. She leaves behind her second husband, Tom Cohen, lead singer of the defunct London punk band S.C.U.M, and two sons, 23-month-old Astala and 11-month-old Phaedra.
"My beloved wife Peaches was adored by myself and her two sons Astala and Phaedra, and I shall bring them up with their mother in their hearts every day. We shall love her forever," Cohen said in a statement.
At age 19 she married Max Drummey, a vocalist with U.S. indie rock band Chester French, at a drive-thru chapel in Las Vegas while the two were on holiday. The marriage lasted six months and ended in 2009.
Friends and acquaintances reacted to news of her death with disbelief.
"It's very, very sad. Peaches has overcome a lot in her childhood, seemed to be getting her life together. You hear something like this and words can fail you. It's just tragic, terrible news," Ray Levine, Peaches' former publicist, told Sky News.
"Having to deal with the death of your mother at such a young age would be difficult for any child, let alone someone in the public spotlight," he added.
In the public eye since her teenage years, Peaches Geldof struggled with a turbulent social life, highlighted at every turn by a British press eager for celebrity news.
Born on March 13, 1989, she left home at 16 and began writing columns for fashion magazines and newspapers, as well as occasional television presenting and modeling. She was well-known among London's young and trendy crowd, frequently snapped wearing cutting-edge outfits on catwalk front rows or on red carpets at movie premieres and exclusive club events.
British tabloids and gossip magazines also focused on the more sordid details of her life, including reports that she was caught shoplifting cosmetics and claims that she used heroin.
In 2010 she was dropped from a lingerie modelling contract after photographs showing her topless and allegations that she used drugs surfaced.
Bob Geldof, 62, rose to fame in the late 1970s as the lead singer of the Irish punk band The Boomtown Rats, but became even better known as a social activist, marshaling the power of his fellow music celebrities — most notably as co-organizer of the 1984 Band-Aid movement and the following year's Live Aid concerts that raised millions for famine relief in Ethiopia.
The fundraising song he co-wrote, "Do they Know It's Christmas?" featuring an ensemble of pop stars remains a radio favorite in Britain and Ireland at Christmastime.
In 2005, he helped organize more celebrity-studded concerts under the banner Live 8 — timed to coincide with a G8 summit taking place in Scotland — that raised funds to fight poverty. For the past decade he has worked alongside fellow Irish rocker Bono at events organized by the U2 singer's anti-poverty charity One.